How long does it take for 2 units of botox to wear off (directly under eye)?

2 units is a very small amount. Although results should last 3 months, they may disappear sooner because the surrounding muscles may slowly take over the function of the paralyzed muscle fibres.  You may need to go back for touchups in less than 3 months.

The treatment under the eyes was off-label. Fortunately, it may be gone as soon as a month, but may linger longer. Time is really your only option.

The length  of time may vary according to how strong the muscles are, consult your plastic surgeon to see if he can help softening the unpleasant results. 

I use Botox under the eye all the time and I find the low dose injections  last around 4-6 weeks approximately. If you have an issue or question You should call your doctor for a reevaluation because maybe you just need more Botox to reduce the other lines. 

The good news is this will go away. The bad news is that there is nothing you can do to make it happen faster. I'd hope just 2 units would be gone within 4-6 weeks. Hang in there. "This answer has been solicited without seeing this patient and
cannot be held as true medical advice, but only opinion. Seek in-person
treatment with a trained medical professional for appropriate care."